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Simplifying x7 + -7x6 + -7x5 = 0 Reorder the terms: -7x5 + -7x6 + x7 = 0 Solving -7x5 + -7x6 + x7 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x5'. x5(-7 + -7x + x2) = 0Subproblem 1
Set the factor 'x5' equal to zero and attempt to solve: Simplifying x5 = 0 Solving x5 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x5 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-7 + -7x + x2)' equal to zero and attempt to solve: Simplifying -7 + -7x + x2 = 0 Solving -7 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -7x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -7x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -7x + x2 = 0 + 7 -7x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -7x + x2 = 7 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 7 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 7 + 12.25 Combine like terms: 7 + 12.25 = 19.25 12.25 + -7x + x2 = 19.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (x + -3.5) equal to 4.387482194 and -4.387482194.Subproblem 1
x + -3.5 = 4.387482194 Simplifying x + -3.5 = 4.387482194 Reorder the terms: -3.5 + x = 4.387482194 Solving -3.5 + x = 4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 4.387482194 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.387482194 + 3.5 x = 4.387482194 + 3.5 Combine like terms: 4.387482194 + 3.5 = 7.887482194 x = 7.887482194 Simplifying x = 7.887482194Subproblem 2
x + -3.5 = -4.387482194 Simplifying x + -3.5 = -4.387482194 Reorder the terms: -3.5 + x = -4.387482194 Solving -3.5 + x = -4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -4.387482194 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.387482194 + 3.5 x = -4.387482194 + 3.5 Combine like terms: -4.387482194 + 3.5 = -0.887482194 x = -0.887482194 Simplifying x = -0.887482194Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.887482194, -0.887482194}Solution
x = {7.887482194, -0.887482194}
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